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3 years ago

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Mathematics

1 answer:

irina [24]3 years ago

5 0

Answer:

61.27 cm

Step-by-step explanation:

refer to picture

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Find lim h to 0 f(1 + h) - f(1) if f(x) = x^2 a. 5 c. 1 b. 4 d. 2

Harman [31]

Answer:

you ouldw get hi,m to 1tdh73n,(6wh+2ufd) 2/56

Step-by-step explanation:

4 0

3 years ago

Use mathematical induction to prove the statement is true for all positive integers n, or show why it is false:

kondaur [170]

$\text{Proof by induction:}$
$\text{Test that the statement holds or n = 1}$

$LHS = (3 - 2)^{2} = 1$
$RHS = \frac{6 - 4}{2} = \frac{2}{2} = 1 = LHS$
$\text{Thus, the statement holds for the base case.}$

$\text{Assume the statement holds for some arbitrary term, n= k}$
$1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2} = \frac{k(6k^{2} - 3k - 1)}{2}$

$\text{Prove it is true for n = k + 1}$
$RTP: 1^{2} + 4^{2} + 7^{2} + ... + [3(k + 1) - 2]^{2} = \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2} = \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$

$LHS = \underbrace{1^{2} + 4^{2} + 7^{2} + ... + (3k - 2)^{2}}_{\frac{k(6k^{2} - 3k - 1)}{2}} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1)}{2} + [3(k + 1) - 2]^{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2[3(k + 1) - 2]^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 2(3k + 1)^{2}}{2}$
$= \frac{k(6k^{2} - 3k - 1) + 18k^{2} + 12k + 2}{2}$
$= \frac{k(6k^{2} - 3k - 1 + 18k + 12) + 2}{2}$
$= \frac{k(6k^{2} + 15k + 11) + 2}{}$
$= \frac{(k + 1)[6k^{2} + 9k + 2]}{2}$
$= \frac{(k + 1)[6(k + 1)^{2} - 3(k + 1) - 1]}{2}$
$= RHS$

Since it is true for n = 1, n = k, and n = k + 1, by the principles of mathematical induction, it is true for all positive values of n.

3 0

3 years ago

What is the equation, in slope-intercept form, of the line that passes through (0, 6) and has a slope of 4?

Arturiano [62]

Y - 6 = 4x
y = 4x + 6

4 0

3 years ago

juan has 48 stamps and 36 stickers. he wants to glue the same number of stamps and the same number of stickers onto 6 pages in h

Alex17521 [72]

14 is the answer, here's how: do 48+36 and get 84 and divide that by 6 and get 14.

3 0

4 years ago

N is an integer

PilotLPTM [1.2K]

Answer:

See below

Step-by-step explanation:

1/2n(n+1) + 1/2(n+1)(n+2) =
1/2(n² + n) + 1/2(n² + 3n + 2) =
1/2(n² + n + n² + 3n + 2) =
1/2(2n² + 4n + 2) =
n² + 2n + 1 =
(n + 1)²

Proved

6 0

3 years ago

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